User blog:HowStrongIs/Size of the Moon (Naruto)
moon scaling 1.png moon scaling 2.jpg The Moon in Naruto is, oddly, hollow. This makes feats involving it very tricky to scale, because they all depend on the thickness of the Moon's crust. Unfortunately for us, there's few shots you can actually scale the Moon's thickness from, with the above two being pretty much all there is. However, it is still possible to get a rough estimate of the Moon's thickness and mass from the above two images. ---- Firstly, we need to get an estimate of how deep the hole is compared to the crater's width based on the second image. This isn't really possible to do, due to the angle, but through eyeballing it and basic scaling it seems that the hole is no less than 10% but no more than 20% as deep as it is wide. From here we just need to scale the width of the crater by comparing it to the rest of the Moon, which will be assumed to have the same width as our own Moon, 3474 km. In order to compare the crater to the full Moon we'll have to get the Moon's radius through the chord method. By scaling from this image we can see that the chord is about 789 px long, while the height to the edge of the circle is about 29 px tall. In addition, the crater is about 224 px long. With all this information in mind the rest is just math. ---- r = ((4*h^2)+(l^2))/(8*h) *h = 29 px *l = 789 px ((4*29^2)+(789^2))/(8*29) = 2698 px d = r*2 *r = 2698 px 2698*2 = 5369 px ---- This gives us a ratio of 1.545 km/px, using the assumed Moon width above. Multiplying that by the crater width shows that the crater is 346 km long. It's depth would also be between 36.4 and 69.2 km, going by the estimates above. After this only the crust's mass is needed. We know the Moon was made from chunks of the Earth, so their densities should be the same. Given that Earth's density is 5.51e12 kg/km^3 '''all we have to do is find the volume of the crust, which can be calculated fairly easily by just subtracting '''36.4 and 69.2 km from the Moon's diameter, solving for that volume, then subtracting that from the regular volume (2.2e10 km^3). To do this we'll have to double the depth figures, to represent that the crust is on both sides of the Moon. ---- 3474 - 69.2 = 3404.8 km V = (4/3)(pi)(r^3) *pi = 3.14 *r = 1702.4 km (4/3)(3.14)(1702.4^3) = 2.07e10 km^3 2.2e10 - 2.07e10 = 1.3e9 km^3 (1.3e9)(5.51e12) = 7.16e21 kg -- 3474 - 138.4 = 3335.6 km V = (4/3)(pi)(r^3) *pi = 3.14 *r = 1667.8 km (4/3)(3.14)(1667.8^3) = 1.94e10 km^3 2.2e10 - 1.94e10 = 2.6e9 km^3 (2.6e9)(5.51e12) = 1.43e22 kg ---- Result *Moon's Mass (10% Estimate) - 3.86e21 kg *Moon's Mass (20% Estimate) - 1.43e22 kg Tidbit: This is how big that crater looks in comparison to the Earth. moon scaling 1 - Copy (2).png ---- Potential Problems With This Calc *As said, the depth is estimated. It isn't a very solid figure, though the true depth is likely between the two estimates. *The calc assumes the Moon in Naruto is the same size as our own. *The dimensions of the crater seem a bit inconsistent, though the crust being thin does seem to be roughly consistent throughout scenes. Category:Blog posts Category:Calculation